Theoretical characterization of the topology of connected carbon nanotubes in random networks

Abstract

In recent years, a lot of attention has been paid to carbon nanotube (CNT) networks and their applications to electronic devices. Many studies concentrate on the percolation threshold and the characterization of the conduction in such materials. Nevertheless, no theoretical study has yet attempted to characterize the CNT features inside finite size CNT networks. We present a theoretical approach based on geometrical and statistical considerations. We demonstrate the possibility of explicitly determining some relations existing between two neighbor CNTs and their contact efficiency in random networks of identical CNTs. We calculate the contact probability of rigid identical CNTs and we obtain a probability of 0.2027, which turns out to be independent of the CNT density. Based on this probability, we establish also the dependence of the number of contacts per CNT as a function of the CNT density. All the theoretical results are validated by very good agreement with Monte Carlo simulations.

Transparent electrodes with nanorings: A computational point of view

“…Numerous works have been devoted to the electrical and optical properties of transparent films with elongated fillers such as NTs, NWs, and nanorods. [3][4][5][6][7][8][9][10][11][12][13][14] However, the use of films containing conducting nanorings [15][16][17] looks extremely attractive since, in this case, there are no dead ends in the percolation cluster, i.e., the percolation cluster is identical to its geometrical backbone. In a two-dimensional continuum percolation, the number density is defined as where N is the number of objects randomly deposited onto a square substrate of size L×L with periodic boundary conditions (PBC).…”

Shielding Effectiveness and Sheet Conductance of Nonwoven Carbon-Fiber Sheets

“…and the number of fibres per unit area will be ݊ , = ܰ ݊ ,,ଵ (16) Using (16) and (13) we can rewrite (15) as…”

“…The number of contacts per fibre predicted by the MCM for a 2D material with truncated Gaussian, non-uniform, angular distributions were compared with the value predicted by Heitz [16] for a uniform angular fibre distribution. For a uniform angular PDF, Heitz's theory fits closely to the MCM results, and for truncated Gaussian PDFs the number of contacts is reduced though it is still proportional to the fibre concentration.…”

“…where ܲ cont = 0.2027 [16]. In practical materials the thickness increases with fibre concentration and it is therefore important to know this relationship if the effect of contact conductance is to be predicted.…”

Shielding effectiveness of non-woven carbon fibre sheets: Modelling the microstructure

“…In Figure 5 we have also plotted the theory of where    p is the angular PDF for the fibres in the material which we have described in detail in [10] and  is the angle of the fibre in the xy-plane, relative to the x-axis. We also considered the average the number of contacts per fibre, which is predicted by Heitz et al [11] for the 2D isotropic case. .…”